Question: Solve for $x$ and $y$ using elimination. ${-2x-5y = -56}$ ${2x+3y = 36}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2x$ and $2x$ cancel out. $-2y = -20$ $\dfrac{-2y}{{-2}} = \dfrac{-20}{{-2}}$ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {-2x-5y = -56}\thinspace$ to find $x$ ${-2x - 5}{(10)}{= -56}$ $-2x-50 = -56$ $-2x-50{+50} = -56{+50}$ $-2x = -6$ $\dfrac{-2x}{{-2}} = \dfrac{-6}{{-2}}$ ${x = 3}$ You can also plug ${y = 10}$ into $\thinspace {2x+3y = 36}\thinspace$ and get the same answer for $x$ : ${2x + 3}{(10)}{= 36}$ ${x = 3}$